Laplace integrals in partial differential equations in papers of Bogdan Ziemian

• Autorzy: Grzegorz Łysik
• Języki publikacji: EN

Abstrakty

EN

Fundamental solutions to linear partial differential equations with constant coefficients are represented in the form of Laplace type integrals.

Słowa kluczowe

EN

Leray residue formula; linear partial differential equations; Nilsson integrals; Laplace representations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 74
• Numer: 1
• Strony: 43-50

Daty

wydano

2000

otrzymano

2000-02-20

Twórcy

autor

Grzegorz Łysik

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland

Bibliografia

• [B] B. L. J. Braaksma, Multisummability of formal power series solutions of nonlinear meromorphic differential equations, Ann. Inst. Fourier (Grenoble) 42 (1992), 517-540.
• [Ec] J. Ecalle, Les fonctions résurgentes, Publ. Math. Univ. de Paris-Sud, 1980.
• [Eh] L. Ehrenpreis, A fundamental principle for systems of linear differential equations with constant coefficients and some of its applications, in: Proc. Internat. Sympos. on Linear Spaces (Jerusalem, 1960), 1961, 161-174.
• [L] J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, Bull. Soc. Math. France 87 (1959), 81-180.
• [NZ] Nguyen Si Minh and B. Ziemian, A remark on Nilsson type integrals, in: Singularities and Differential Equations, Banach Center Publ. 33, Inst. Math., Polish Acad. Sci., Warszawa, 1996, 227-285.
• [N] N. Nilsson, Some growth and ramification properties of certain multiple integrals, Ark. Mat. 5 (1965), 463-476.
• [P] V. P. Palamodov, General form of solutions of linear differential operators with constant coefficients, Dokl. Akad. Nauk SSSR 143 (1962), 1278-1281 (in Russian).
• [SZ] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Math. Appl. 56, Kluwer, 1992.
• [Z1] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293.
• [Z2] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).